Sixty percent of new cars will be connected by 2017

Global OEM connected car system penetration is expected to increase from 11.4 percent in 2012 to 60.1 percent in 2017. While penetration in the US and Western Europe will exceed 80% by 2017, developing regions such as Latin America and Eastern Europe will also see strong increases in telematics penetration in new vehicles, largely driven by mandates in Brazil and Russia.

I agree that if humans were behind the wheel, then your fears would be well justified and driving through such an intersection would be sheer terror. However, I think overtime as autonomous vehicles demonstrate their vastly superior driving accuracy, we the passengers will consider our cars as operating on virtual rails and as such are fears of accidents will largely vanish. At this point, we won't give a second thought to navigating through such an intersection.

Hmmm... are the windows in the cars made to be opaque, or do we just accept a certain number of heart attacks as another car comes within a few feet of T-boning you at full speed.
I suspect that adjusting speeds so that clumps of cars go through in each direction with a bit less near miss cross flow would be much easier on the nerves with little loss in overall efficiency.

On the one hand, connectivity in cars has been gradually increasing ever since the car radio was first developed. But I assume here that we're talking about two-way comms between cars. I agree. That will be commonplace, and also comms between the car and the road.
Here's what I find intriguing. Some might predict that controlling traffic algorithimcally is a tremendously difficult problem. But perhaps it depends how this is done.
Look at the grains of sand flowing through an hourglass. They seem to find their way through very efficiently, with no need for an explicit algorithm to control their movement.
So one approach might be, just have each car know where it wants to go, and then have each car apply constant "pressure" on the surrounding traffic, until it gets to the destination. The comms between vehicles keeps a safe distance at all times, and the comms with the road funnel the cars along valid paths to each one's destination.
This approach would seem to be self regulating in the event of traffic congestion. Much like the grains of sand in a mostly empty hourglass will quickly get to the other side, whereas some of them will take a lot longer if the hourglass is full.

Not only can I imagine it but the following site shows a video of how an intersection without any traffic lights could function with connected vehicles. Clearly the days of human driven vehicles on public thoroughfares are limited and I for one look forward to it. See here, http://www.driverlesscarhq.com/elimination-of-traffic-lights-one-step-closer/ .

It is very safe to argue that if Apple strikes a deal to equip car models with iPhone or iPad clones for autos, we can get to 90% faster. Connectivity is going to become common and any company not playing into that cannot compete.

The idea that the key to design will be in how to manage swarm behavior was one i heard from UCB academic Alberto Sangiovanni-Vincentelli not too long ago.
Imagine a swarm of connected cars, faster reacting than any individual driver and more intelligent?